Skip to main content

Full text of "Mathematical And Physical Papers - Iii"

See other formats


ON" THE  MOTION  OF PENDULUMS.
79
Determination of yX by means of Baily's experiments with plain cylindrical rods.
Pendulum rod		No.	Diameter 2a	Time of vibration T	ti by experiment
Copper, Brass, Steel,	58*8 inches long 56-4 ...............	21 43 44	0'410 0'185 0-072	1-0136 0-9933 0-9933	2-932 4-083 7'530
	56-4 ...............				
					
No.	Correction for confined space (by theory)	Deduced value of k by experiment	Corresponding value of m	Resulting value of VM-'
21	-0-009	1-923	1-5445	0*1166
43	-0-002	3-081	'0-7000	0-1175
44		6-530	0-2822	0-1134
In  this  table  the first  column  explains  itself.     The   next contains the reference number.    In the case of the copper rod I have replaced 42 by 21, under which number the details of the experiment will be found.    The diameters  of the rods are expressed in decimals of an inch.    The time of vibration of the pendulum  No. 21  may be  got  from the tables at the end of Baily's memoir, which contain the  details  of the  experiments. Nos. 43 and 44 belong to the " additional experiments," of which all the details are suppressed.    JBaily has not  even  given  the times of vibration, not having been aware of the circumstance, indicated by the  theory of this  paper, that  the  factor n and the weight of air which must be conceived as dragged by the pendulum are functions of the time of vibration.    Accordingly, in the cases of the pendulums Nos. 43 and 44, and in all similar cases, I have calculated the time of vibration by the ordinary formulae of dynamics.    In calculating T, I have added T55 inch, the length of the shank of the knife-edge apparatus, to the length of the rods.   The result so obtained is abundantly accurate enough for my purpose.    Had the rod, retaining its actual length, been supposed to begin directly at the knife-edge, the error thence